Sequences and Series
Find x, if 2,x,21 are in G.P.
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Find the sum to n
terms of the sequence (x+1/x)2,(x2+1/x)2,(x3+1/x)2,,
If eleven A.M. ‘s are inserted between 28 and 10, then find the number of integral A.M. ‘s.
Find the sum 23−65+187−549+∞˙
e the sum, P
the product, adn R
the sum of reciprocals of n
terms in a G.P. Prove that P2Rn=Sn˙
Find the value of n so that an+bnan+1+bn+1 may be the geometric mean between a and b.
are respectively, the pth, qth , and rth terms of a G.P., show that (q−r)loga+(r−p)logb+(p−q)logc=0.
Three numbers are in G.P. whose sum is 70. If the extremes be each multiplied by 4 and the means by 5, they will be in A.P. Find the numbers.
are in A.P., then prove that the following are also in A.P.